Metrics for ENA, Section 1.4, Mentioned, A

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze4.0ms (0.1%)

Memory

7.4MiB live, 7.4MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	49.6%	50.4%	0%	0%	0%	0
0%	0%	49.6%	50.4%	0%	0%	0%	1
0%	0%	49.6%	50.4%	0%	0%	0%	2
50%	24.8%	24.8%	50.4%	0%	0%	0%	3
75%	37.2%	12.4%	50.4%	0%	0%	0%	4
87.5%	43.4%	6.2%	50.4%	0%	0%	0%	5
93.8%	46.5%	3.1%	50.4%	0%	0%	0%	6
96.9%	48.1%	1.6%	50.4%	0%	0%	0%	7
98.4%	48.8%	0.8%	50.4%	0%	0%	0%	8
99.2%	49.2%	0.4%	50.4%	0%	0%	0%	9
99.6%	49.4%	0.2%	50.4%	0%	0%	0%	10
99.8%	49.5%	0.1%	50.4%	0%	0%	0%	11
99.9%	49.6%	0%	50.4%	0%	0%	0%	12

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample3.0s (51%)

Memory

-9.8MiB live, 3 719.4MiB allocated

Samples

2.1s	5 675×	2	valid
535.0ms	2 500×	1	valid
6.0ms	81×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 2.1s

ival-cos: 1.3s (62.9% of total)

const: 297.0ms (14.1% of total)

adjust: 231.0ms (11% of total)

ival-sub: 171.0ms (8.1% of total)

ival-<=: 60.0ms (2.9% of total)

ival-and: 12.0ms (0.6% of total)

exact: 5.0ms (0.2% of total)

ival-assert: 3.0ms (0.1% of total)

Bogosity

explain177.0ms (3%)

Memory

30.0MiB live, 220.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
137	-	-	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(cos.f64 x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	137	0

Confusion

	Predicted +	Predicted -
+	137	0
-	0	119

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	137	0	0
-	0	0	119

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	119
1	137

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

81.0ms	358×	2	valid
12.0ms	146×	1	valid
0.0ms	8×	0	valid

Compiler

Compiled 24 to 16 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 75.0ms

ival-cos: 56.0ms (75% of total)

adjust: 10.0ms (13.4% of total)

ival-sub: 7.0ms (9.4% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

preprocess15.0ms (0.3%)

Memory

-18.0MiB live, 28.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	16	9
2	24	9
3	25	9
0	4	4
0	6	4
1	15	4
2	21	4
3	26	4
0	26	4

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(-.f64 #s(literal 1 binary64) (cos.f64 x))

Outputs
(-.f64 #s(literal 1 binary64) (cos.f64 x))

Symmetry

(abs x)

Compiler

Compiled 4 to 4 computations (0% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.2%	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Compiler

Compiled 4 to 4 computations (0% saved)

simplify3.0ms (0.1%)

Memory

4.4MiB live, 4.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(cos.f64 x)
cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	15	8
2	21	8
3	26	8
0	26	8

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x

Outputs
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x

localize49.0ms (0.8%)

Memory

13.0MiB live, 13.0MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(cos.f64 x)
accuracy	31.234912922716354	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

37.0ms	179×	2	valid
6.0ms	73×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 10 to 6 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-cos: 25.0ms (74.1% of total)

adjust: 5.0ms (14.8% of total)

ival-sub: 3.0ms (8.9% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series1.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Counts

2 → 10

Calls

Call 1

Inputs
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)

Outputs
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(- 1 (cos x))
(cos x)

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	((- 1 (cos x)) (cos x))
0.0ms	x	@	inf	((- 1 (cos x)) (cos x))
0.0ms	x	@	-inf	((- 1 (cos x)) (cos x))

simplify161.0ms (2.7%)

Memory

-26.1MiB live, 168.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	102
1	119	102
2	317	102
3	1130	102
4	2687	102
5	4996	102
0	8365	90

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 10

Calls

Call 1

Inputs
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(- 1 (cos x))
(cos x)

Outputs
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 (fma.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/40320 binary64) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)))) x #s(literal 1/2 binary64)) x) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos x)
(cos.f64 x)

rewrite192.0ms (3.3%)

Memory

30.3MiB live, 173.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
0	6	6
1	29	6
2	223	6
3	2247	6
0	8760	6

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

2 → 158

Calls

Call 1

Inputs
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)

Outputs
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) (cos.f64 x) #s(literal -1 binary64)))
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) (-.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (neg.f64 (sin.f64 x)) (tan.f64 (/.f64 (neg.f64 x) #s(literal 2 binary64))))
(*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -2 binary64)) (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) (neg.f64 (/.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -2 binary64)) (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))) #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) (cos.f64 x) #s(literal -1 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -3 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 3 binary64))))) (neg.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -3 binary64)) (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))) #s(literal 2 binary64)) (*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal -1 binary64) (cos.f64 x) #s(literal -1 binary64)))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (neg.f64 (neg.f64 (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (neg.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 2 binary64))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))) (.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (neg.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)))))
(/.f64 (-.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal -1 binary64) (cos.f64 x) #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -2 binary64)) (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64))) (/.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (-.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -2 binary64)) (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -3 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 6 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 3 binary64)))) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))))
(/.f64 (-.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -3 binary64)) (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))) #s(literal 2 binary64)) (*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 9 binary64)))) (neg.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (neg.f64 (*.f64 (fma.f64 (cos.f64 x) (cos.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (cos.f64 x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) (neg.f64 (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (neg.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
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(fabs.f64 (cos.f64 x))
(cos.f64 (neg.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (neg.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(cos.f64 (asin.f64 (fabs.f64 (sin.f64 x))))
(cos.f64 (asin.f64 (neg.f64 (sin.f64 x))))
(cos.f64 (asin.f64 (sin.f64 x)))
(cos.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(exp.f64 (/.f64 (log.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (cos.f64 x)))
(+.f64 (.f64 (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (.f64 x x)))) (cos.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (.f64 x x))))) (.f64 (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (.f64 x x)))) (sin.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (.f64 x x))))))
(+.f64 (cosh.f64 (log.f64 (cos.f64 x))) (sinh.f64 (log.f64 (cos.f64 x))))
(+.f64 (.f64 (.f64 #s(literal 0 binary64) (sin.f64 x)) #s(literal 1 binary64)) (cos.f64 x))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal 0 binary64) (sin.f64 x))) (cos.f64 x))
(+.f64 (*.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (cos.f64 x))
(+.f64 (*.f64 #s(literal 0 binary64) (sin.f64 x)) (cos.f64 x))
(+.f64 (cos.f64 x) (*.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))))
(+.f64 (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))

eval19.0ms (0.3%)

Memory: -0.1MiB live, 45.6MiB allocated
Compiler: Compiled 2 937 to 564 computations (80.8% saved)

prune23.0ms (0.4%)

Memory

-52.5MiB live, 13.2MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	162	6	168
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	6	169

Accuracy

100.0%

Counts

169 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	51.2%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
▶	50.9%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
▶	50.1%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
▶	100.0%	#s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))
▶	99.8%	#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
▶	99.3%	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))

Compiler

Compiled 156 to 112 computations (28.2% saved)

simplify297.0ms (5%)

Memory

36.4MiB live, 351.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
cost-diff	0	(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
cost-diff	0	(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
cost-diff	0	#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
cost-diff	0	#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 (.f64 x x) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
cost-diff	0	#s(approx (cos x) #s(literal 1 binary64))
cost-diff	0	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
cost-diff	0	(.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x))
cost-diff	0	#s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	170
0	41	170
1	83	170
2	256	170
3	1021	170
4	3084	170
5	4203	170
6	5145	170
7	6620	170
0	8415	170

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))
(.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x))
(fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x x)
x
(fma.f64 (*.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64))
(*.f64 #s(literal 1/720 binary64) x)
#s(literal 1/720 binary64)
#s(literal -1/24 binary64)
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
x
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(literal 1 binary64)
#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
#s(literal -1/2 binary64)
(*.f64 x x)
x
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
#s(literal -1/24 binary64)
(*.f64 x x)
x
#s(literal 1/2 binary64)

Outputs
#s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x))
(.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x))
(.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x)
(fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(fma.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(*.f64 x x)
x
(fma.f64 (*.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64))
(*.f64 #s(literal 1/720 binary64) x)
#s(literal 1/720 binary64)
#s(literal -1/24 binary64)
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
#s(approx (- 1 (cos x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(*.f64 x x)
x
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(literal 1 binary64)
#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
#s(literal -1/2 binary64)
(*.f64 x x)
x
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
#s(literal -1/24 binary64)
(*.f64 x x)
x
#s(literal 1/2 binary64)

localize232.0ms (3.9%)

Memory

-9.9MiB live, 247.4MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.00390625	(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
accuracy	0.0078125	(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
accuracy	0.145165292605937	#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
accuracy	0.0	(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	0.19395941124494892	#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
accuracy	31.234912922716354	(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
accuracy	0.0	(*.f64 x x)
accuracy	0.0078125	(.f64 (.f64 x x) #s(literal 1/2 binary64))
accuracy	0.46491552181544016	#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
accuracy	0.5085121162443544	#s(approx (cos x) #s(literal 1 binary64))
accuracy	31.234912922716354	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
accuracy	0.0	#s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))
accuracy	0.00390625	(fma.f64 (*.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64))
accuracy	0.0078125	(.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x))
accuracy	0.2421875	(*.f64 #s(literal 1/720 binary64) x)

Samples

146.0ms	179×	2	valid
68.0ms	73×	1	valid
1.0ms	4×	0	valid

Compiler

Compiled 130 to 24 computations (81.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 167.0ms

ival-add: 52.0ms (31.2% of total)

adjust: 45.0ms (27% of total)

ival-mult: 29.0ms (17.4% of total)

ival-cos: 26.0ms (15.6% of total)

const: 10.0ms (6% of total)

ival-sub: 4.0ms (2.4% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series8.0ms (0.1%)

Memory

21.8MiB live, 21.8MiB allocated

Counts

17 → 36

Calls

Call 1

Inputs
#s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))
(.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x))
(fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x x)
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/720 binary64) x)
(fma.f64 (*.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64))

Outputs
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(pow x 2)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* 1/720 x)
-1/24
(- (* 1/720 (pow x 2)) 1/24)
(- 1 (cos x))
(* 1/720 (pow x 6))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 4))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(cos x)
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* 1/720 (pow x 2))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	((- 1 (cos x)) (* (+ (* (* x x) (+ (* (* 1/720 x) x) -1/24)) 1/2) (* x x)) (+ (* (* x x) (+ (* (* 1/720 x) x) -1/24)) 1/2) (* x x) (- 1 (cos x)) (cos x) (- 1 (cos x)) (* (* x x) 1/2) (- 1 (cos x)) (cos x) (+ (* -1/2 (* x x)) 1) (- 1 (cos x)) (* (* (+ (* -1/24 (* x x)) 1/2) x) x) (* (+ (* -1/24 (* x x)) 1/2) x) (+ (* -1/24 (* x x)) 1/2) (* 1/720 x) (+ (* (* 1/720 x) x) -1/24))
2.0ms	x	@	-inf	((- 1 (cos x)) (* (+ (* (* x x) (+ (* (* 1/720 x) x) -1/24)) 1/2) (* x x)) (+ (* (* x x) (+ (* (* 1/720 x) x) -1/24)) 1/2) (* x x) (- 1 (cos x)) (cos x) (- 1 (cos x)) (* (* x x) 1/2) (- 1 (cos x)) (cos x) (+ (* -1/2 (* x x)) 1) (- 1 (cos x)) (* (* (+ (* -1/24 (* x x)) 1/2) x) x) (* (+ (* -1/24 (* x x)) 1/2) x) (+ (* -1/24 (* x x)) 1/2) (* 1/720 x) (+ (* (* 1/720 x) x) -1/24))
2.0ms	x	@	0	((- 1 (cos x)) (* (+ (* (* x x) (+ (* (* 1/720 x) x) -1/24)) 1/2) (* x x)) (+ (* (* x x) (+ (* (* 1/720 x) x) -1/24)) 1/2) (* x x) (- 1 (cos x)) (cos x) (- 1 (cos x)) (* (* x x) 1/2) (- 1 (cos x)) (cos x) (+ (* -1/2 (* x x)) 1) (- 1 (cos x)) (* (* (+ (* -1/24 (* x x)) 1/2) x) x) (* (+ (* -1/24 (* x x)) 1/2) x) (+ (* -1/24 (* x x)) 1/2) (* 1/720 x) (+ (* (* 1/720 x) x) -1/24))

Time

Variable

Point

Expression

3.0ms

inf

((- 1 (cos x)) (* (+ (* (* x x) (+ (* (* 1/720 x) x) -1/24)) 1/2) (* x x)) (+ (* (* x x) (+ (* (* 1/720 x) x) -1/24)) 1/2) (* x x) (- 1 (cos x)) (cos x) (- 1 (cos x)) (* (* x x) 1/2) (- 1 (cos x)) (cos x) (+ (* -1/2 (* x x)) 1) (- 1 (cos x)) (* (* (+ (* -1/24 (* x x)) 1/2) x) x) (* (+ (* -1/24 (* x x)) 1/2) x) (+ (* -1/24 (* x x)) 1/2) (* 1/720 x) (+ (* (* 1/720 x) x) -1/24))

2.0ms

-inf

((- 1 (cos x)) (* (+ (* (* x x) (+ (* (* 1/720 x) x) -1/24)) 1/2) (* x x)) (+ (* (* x x) (+ (* (* 1/720 x) x) -1/24)) 1/2) (* x x) (- 1 (cos x)) (cos x) (- 1 (cos x)) (* (* x x) 1/2) (- 1 (cos x)) (cos x) (+ (* -1/2 (* x x)) 1) (- 1 (cos x)) (* (* (+ (* -1/24 (* x x)) 1/2) x) x) (* (+ (* -1/24 (* x x)) 1/2) x) (+ (* -1/24 (* x x)) 1/2) (* 1/720 x) (+ (* (* 1/720 x) x) -1/24))

2.0ms

((- 1 (cos x)) (* (+ (* (* x x) (+ (* (* 1/720 x) x) -1/24)) 1/2) (* x x)) (+ (* (* x x) (+ (* (* 1/720 x) x) -1/24)) 1/2) (* x x) (- 1 (cos x)) (cos x) (- 1 (cos x)) (* (* x x) 1/2) (- 1 (cos x)) (cos x) (+ (* -1/2 (* x x)) 1) (- 1 (cos x)) (* (* (+ (* -1/24 (* x x)) 1/2) x) x) (* (+ (* -1/24 (* x x)) 1/2) x) (+ (* -1/24 (* x x)) 1/2) (* 1/720 x) (+ (* (* 1/720 x) x) -1/24))

simplify185.0ms (3.1%)

Memory

4.6MiB live, 137.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	303
1	198	303
2	505	303
3	1812	302
4	5257	302
0	8331	283

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(pow x 2)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* 1/720 x)
-1/24
(- (* 1/720 (pow x 2)) 1/24)
(- 1 (cos x))
(* 1/720 (pow x 6))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* 1/720 (pow x 4))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(cos x)
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1/24 (pow x 4))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* 1/720 (pow x 2))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))

Outputs
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/40320 binary64) (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64))) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(fma.f64 (fma.f64 #s(literal 1/720 binary64) (.f64 x x) #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/720 binary64)) #s(literal 1/2 binary64)) x (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/24 binary64))) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(* 1/720 x)
(*.f64 #s(literal 1/720 binary64) x)
-1/24
#s(literal -1/24 binary64)
(- (* 1/720 (pow x 2)) 1/24)
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(* 1/720 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/720 binary64))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/720 binary64)) (/.f64 #s(literal 1/24 binary64) (.f64 x x))) (pow.f64 x #s(literal 6 binary64)))
(* 1/720 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/720 binary64))
(* (pow x 4) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64)) x) x)
(* (pow x 4) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 (.f64 #s(literal -1/24 binary64) x) x (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/720 binary64)) (pow.f64 x #s(literal 4 binary64))))
(cos x)
(cos.f64 x)
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) x)
(* -1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64))
(* (pow x 4) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)) (pow.f64 x #s(literal 4 binary64)))
(* -1/24 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/24 binary64))
(* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)))
(* -1/24 (pow x 2))
(.f64 #s(literal -1/24 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1/24 binary64)) (*.f64 x x))
(* 1/720 (pow x 2))
(.f64 #s(literal 1/720 binary64) (.f64 x x))
(* (pow x 2) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
(* -1 (* (pow x 3) (- 1/24 (* 1/2 (/ 1 (pow x 2))))))
(.f64 (-.f64 #s(literal -1/24 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (pow.f64 x #s(literal 3 binary64)))

rewrite278.0ms (4.7%)

Memory

-28.1MiB live, 159.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	148
0	41	148
1	166	148
2	1224	148
0	8367	148

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

17 → 408

Calls

Call 1

Inputs
#s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))
(.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x))
(fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x x)
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
(.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)
(.f64 (fma.f64 #s(literal -1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/720 binary64) x)
(fma.f64 (*.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64))

Outputs
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x))
(.f64 (.f64 (neg.f64 x) (fma.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))) (neg.f64 x))
(.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x) x)
(.f64 (neg.f64 x) (.f64 (neg.f64 x) (fma.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (.f64 x x))
(.f64 (.f64 x x) (fma.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)))
(.f64 x (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x) (.f64 x x)) (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x) (.f64 x x))) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))) (-.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x)) (.f64 (.f64 x x) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x))) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x)) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x) (.f64 x x)) (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x) (.f64 x x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x) (*.f64 x x))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (.f64 x x) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x)) (.f64 (.f64 x x) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x)))) (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x) (.f64 x x)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x) (.f64 x x)) (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x) (.f64 x x)) (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x)) (.f64 (.f64 x x) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x)) (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (.f64 (.f64 x x) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x) (.f64 x x)) #s(literal 3 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x) (.f64 x x)) (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x) (.f64 x x))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x) (.f64 x x))))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 x x) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x)) #s(literal 3 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x)) (.f64 (.f64 x x) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) x) x))))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (pow.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (.f64 x x))) (neg.f64 (fma.f64 #s(literal 1/720 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 #s(literal -1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) (.f64 x x))) (neg.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (-.f64 (.f64 (pow.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)))) (neg.f64 (fma.f64 #s(literal 1/720 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 #s(literal -1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (-.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x))))))
(/.f64 (.f64 (-.f64 (.f64 (pow.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (.f64 x x)) (fma.f64 #s(literal 1/720 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 #s(literal -1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))))
(/.f64 (.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64)) (.f64 x x)) (-.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
(/.f64 (.f64 (.f64 x x) (-.f64 (.f64 (pow.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64))) (fma.f64 #s(literal 1/720 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 #s(literal -1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))))
(/.f64 (.f64 (.f64 x x) (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1/8 binary64))) (-.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x x)))))
(neg.f64 (.f64 (.f64 (neg.f64 x) (fma.f64 (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))) x))
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(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/576 binary64) (-.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))) (/.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))) (fma.f64 (/.f64 #s(literal 1/576 binary64) (-.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (-.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))) (.f64 (/.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (-.f64 (.f64 (*.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64)))))))
(/.f64 (-.f64 #s(literal -1/13824 binary64) (pow.f64 (.f64 #s(literal -1/720 binary64) (.f64 x x)) #s(literal 3 binary64))) (+.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -1/24 binary64) (.f64 #s(literal -1/720 binary64) (*.f64 x x))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -1/13824 binary64) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))))) (/.f64 (.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))))) (-.f64 (.f64 (/.f64 #s(literal -1/13824 binary64) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))))) (/.f64 #s(literal -1/13824 binary64) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64)))))) (.f64 (/.f64 (.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))))) (/.f64 #s(literal -1/13824 binary64) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64)))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (-.f64 #s(literal -1/24 binary64) (.f64 (*.f64 #s(literal 1/720 binary64) x) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/576 binary64)))) (neg.f64 (neg.f64 (-.f64 (.f64 (*.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/13824 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (*.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))) (.f64 (-.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64)) #s(literal 1/576 binary64))) (.f64 (-.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64)) (-.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))))
(/.f64 (fma.f64 (.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64)))) (.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64)))) #s(literal -1/13824 binary64))) (.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64)))) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (*.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))))))
(/.f64 (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal -1/24 binary64) (.f64 (*.f64 #s(literal 1/720 binary64) x) x)))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/576 binary64))) (neg.f64 (-.f64 (.f64 (*.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/13824 binary64))) (neg.f64 (+.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 1/24 binary64) (.f64 (*.f64 #s(literal 1/720 binary64) x) x))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/13824 binary64))) (neg.f64 (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (*.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))))))
(/.f64 (-.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/576 binary64)) (-.f64 (.f64 (*.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64)))
(/.f64 (fma.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/13824 binary64)) (+.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 1/24 binary64) (.f64 (*.f64 #s(literal 1/720 binary64) x) x)))))
(/.f64 (fma.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64)) #s(literal -1/13824 binary64)) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (*.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64)))))
(fma.f64 (fabs.f64 (*.f64 #s(literal -1/720 binary64) x)) x #s(literal -1/24 binary64))
(fma.f64 (fabs.f64 (*.f64 #s(literal 1/720 binary64) x)) x #s(literal -1/24 binary64))
(fma.f64 (*.f64 #s(literal -1/720 binary64) x) (neg.f64 x) #s(literal -1/24 binary64))
(fma.f64 (*.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64))
(fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))
(fma.f64 x (fabs.f64 (*.f64 #s(literal 1/720 binary64) x)) #s(literal -1/24 binary64))
(fma.f64 x (*.f64 #s(literal 1/720 binary64) x) #s(literal -1/24 binary64))
(-.f64 (/.f64 #s(literal 1/576 binary64) (-.f64 #s(literal -1/24 binary64) (.f64 (.f64 #s(literal 1/720 binary64) x) x))) (/.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal -1/24 binary64) (.f64 (*.f64 #s(literal 1/720 binary64) x) x))))
(-.f64 (/.f64 (.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (-.f64 (.f64 (*.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))))
(-.f64 #s(literal -1/24 binary64) (.f64 #s(literal -1/720 binary64) (.f64 x x)))
(+.f64 (/.f64 #s(literal -1/13824 binary64) (+.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 #s(literal 1/720 binary64) x) x))))) (/.f64 (.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 1/24 binary64) (.f64 (*.f64 #s(literal 1/720 binary64) x) x))))))
(+.f64 (/.f64 (.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 #s(literal 1/720 binary64) x) x))))) (/.f64 #s(literal -1/13824 binary64) (+.f64 #s(literal 1/576 binary64) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal 1/24 binary64) (.f64 (*.f64 #s(literal 1/720 binary64) x) x))))))
(+.f64 (/.f64 #s(literal -1/13824 binary64) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))))) (/.f64 (.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (*.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))))))
(+.f64 (/.f64 (.f64 #s(literal 1/373248000 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))))) (/.f64 #s(literal -1/13824 binary64) (fma.f64 #s(literal 1/518400 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (*.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))))))
(+.f64 (.f64 (.f64 #s(literal 1/720 binary64) x) x) #s(literal -1/24 binary64))
(+.f64 #s(literal -1/24 binary64) (.f64 (neg.f64 (.f64 #s(literal -1/720 binary64) x)) x))
(+.f64 #s(literal -1/24 binary64) (.f64 (neg.f64 (neg.f64 x)) (.f64 #s(literal 1/720 binary64) x)))
(+.f64 #s(literal -1/24 binary64) (.f64 (.f64 #s(literal 1/720 binary64) x) x))

eval156.0ms (2.6%)

Memory: 18.0MiB live, 75.0MiB allocated
Compiler: Compiled 15 931 to 1 979 computations (87.6% saved)

prune21.0ms (0.4%)

Memory

-20.0MiB live, 26.6MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	520	1	521
Fresh	0	1	1
Picked	1	4	5
Done	0	0	0
Total	521	6	527

Accuracy

100.0%

Counts

527 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.2%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
✓	50.9%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
✓	50.1%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
✓	100.0%	#s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))
✓	99.8%	#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
▶	99.3%	#s(approx (- 1 (cos x)) (.f64 (.f64 #s(literal 1/2 binary64) x) x))

Compiler

Compiled 78 to 56 computations (28.2% saved)

simplify31.0ms (0.5%)

Memory

34.7MiB live, 34.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))
cost-diff	0	#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(.f64 (.f64 #s(literal 1/2 binary64) x) x)
cost-diff	0	#s(approx (- 1 (cos x)) (.f64 (.f64 #s(literal 1/2 binary64) x) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	77
0	25	77
1	54	77
2	167	77
3	675	77
4	1469	77
5	1615	77
6	1644	77
7	1659	77
8	1659	77
0	1659	77

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- 1 (cos x)) (.f64 (.f64 #s(literal 1/2 binary64) x) x))
(.f64 (.f64 #s(literal 1/2 binary64) x) x)
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(literal 1 binary64)
#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 x x)
x
(fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))
(*.f64 #s(literal 1/24 binary64) x)
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)

Outputs
#s(approx (- 1 (cos x)) (.f64 (.f64 #s(literal 1/2 binary64) x) x))
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1/2 binary64) x) x)
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(literal 1 binary64)
#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
x
(fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64))
(*.f64 #s(literal 1/24 binary64) x)
#s(literal 1/24 binary64)
#s(literal -1/2 binary64)

localize123.0ms (2.1%)

Memory

-48.5MiB live, 101.6MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.010097509768442016	#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
accuracy	0.3359375	(*.f64 #s(literal 1/24 binary64) x)
accuracy	31.234912922716354	(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
accuracy	0.0	(.f64 (.f64 #s(literal 1/2 binary64) x) x)
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.46491552181544016	#s(approx (- 1 (cos x)) (.f64 (.f64 #s(literal 1/2 binary64) x) x))

Samples

93.0ms	179×	2	valid
13.0ms	73×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 52 to 17 computations (67.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 87.0ms

ival-cos: 35.0ms (40.4% of total)

adjust: 32.0ms (37% of total)

ival-mult: 9.0ms (10.4% of total)

ival-sub: 4.0ms (4.6% of total)

const: 4.0ms (4.6% of total)

ival-add: 2.0ms (2.3% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

2.3MiB live, 2.3MiB allocated

Counts

8 → 16

Calls

Call 1

Inputs
#s(approx (- 1 (cos x)) (.f64 (.f64 #s(literal 1/2 binary64) x) x))
(.f64 (.f64 #s(literal 1/2 binary64) x) x)
(*.f64 #s(literal 1/2 binary64) x)
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 x x)
(*.f64 #s(literal 1/24 binary64) x)

Outputs
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* 1/2 x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(pow x 2)
(* 1/24 x)
(- 1 (cos x))
(cos x)
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

((- 1 (cos x)) (* (* 1/2 x) x) (* 1/2 x) (- 1 (cos x)) (cos x) (+ (* (* x x) (+ (* (* 1/24 x) x) -1/2)) 1) (* x x) (* 1/24 x))

1.0ms

-inf

((- 1 (cos x)) (* (* 1/2 x) x) (* 1/2 x) (- 1 (cos x)) (cos x) (+ (* (* x x) (+ (* (* 1/24 x) x) -1/2)) 1) (* x x) (* 1/24 x))

1.0ms

((- 1 (cos x)) (* (* 1/2 x) x) (* 1/2 x) (- 1 (cos x)) (cos x) (+ (* (* x x) (+ (* (* 1/24 x) x) -1/2)) 1) (* x x) (* 1/24 x))

simplify157.0ms (2.7%)

Memory

20.8MiB live, 102.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	144
1	147	144
2	370	144
3	1285	140
4	3246	140
5	6329	140
0	8085	127

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 16

Calls

Call 1

Inputs
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* 1/2 x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(pow x 2)
(* 1/24 x)
(- 1 (cos x))
(cos x)
(* 1/24 (pow x 4))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))

Outputs
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (fma.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/40320 binary64) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)))) x #s(literal 1/2 binary64)) (.f64 x x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* 1/24 x)
(*.f64 #s(literal 1/24 binary64) x)
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos x)
(cos.f64 x)
(* 1/24 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64))
(* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (-.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))

rewrite181.0ms (3.1%)

Memory

23.5MiB live, 204.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	65
0	25	65
1	103	65
2	785	65
0	8399	65

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

8 → 173

Calls

Call 1

Inputs
#s(approx (- 1 (cos x)) (.f64 (.f64 #s(literal 1/2 binary64) x) x))
(.f64 (.f64 #s(literal 1/2 binary64) x) x)
(*.f64 #s(literal 1/2 binary64) x)
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 x x)
(*.f64 #s(literal 1/24 binary64) x)

Outputs
#s(approx (- 1 (cos x)) (.f64 (.f64 #s(literal 1/2 binary64) x) x))
(.f64 (.f64 #s(literal 1/2 binary64) (neg.f64 x)) (neg.f64 x))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 1/2 binary64)))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 #s(literal 1/2 binary64) x) x)
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 x (.f64 #s(literal 1/2 binary64) x))
(neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) (neg.f64 x)) x))
(neg.f64 (.f64 #s(literal 1/2 binary64) (.f64 (neg.f64 x) x)))
(neg.f64 (.f64 (.f64 (neg.f64 x) x) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 2 binary64)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (pow.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 2 binary64)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) #s(literal 2 binary64)))) (-.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) (pow.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (pow.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 2 binary64)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 (pow.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 2 binary64)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 2 binary64)) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (-.f64 (.f64 (pow.f64 (+.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))) (.f64 (/.f64 (pow.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 (pow.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64))))) (+.f64 (pow.f64 (+.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)))))
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(+.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/24 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(+.f64 (pow.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x) x))) #s(literal -1 binary64)) (/.f64 (.f64 (pow.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x) x)))))
(+.f64 (/.f64 (.f64 (pow.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x) x)))) (pow.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x) x))) #s(literal -1 binary64)))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64) #s(literal 1 binary64)))
(+.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64)) (fma.f64 (.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)))
(+.f64 (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) x) x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 x (.f64 x #s(literal 1 binary64)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (.f64 (.f64 (neg.f64 x) x) #s(literal 1 binary64)))
(neg.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 x #s(literal 1/24 binary64))

eval38.0ms (0.6%)

Memory: -1.7MiB live, 44.3MiB allocated
Compiler: Compiled 8 034 to 842 computations (89.5% saved)

prune6.0ms (0.1%)

Memory

15.8MiB live, 15.8MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	189	6	195

Accuracy

100.0%

Counts

195 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.2%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
✓	50.9%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
✓	50.1%	(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
✓	100.0%	#s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))
✓	99.8%	#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
✓	99.3%	#s(approx (- 1 (cos x)) (.f64 (.f64 #s(literal 1/2 binary64) x) x))

Compiler

Compiled 170 to 93 computations (45.3% saved)

regimes19.0ms (0.3%)

Memory

-41.7MiB live, 14.2MiB allocated

Counts

8 → 1

Calls

Call 1

Inputs
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- 1 (cos x)) (.f64 (.f64 #s(literal 1/2 binary64) x) x))
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))

Outputs
#s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))

Calls

3 calls:

14.0ms	(cos.f64 x)
3.0ms	x
2.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Results

Accuracy	Segments	Branch
100.0%	1	`(cos.f64 x)`
100.0%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
100.0%	1	`x`

Compiler

Compiled 7 to 7 computations (0% saved)

regimes6.0ms (0.1%)

Memory

14.6MiB live, 14.6MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- 1 (cos x)) (.f64 (.f64 #s(literal 1/2 binary64) x) x))
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/24 binary64) x) x #s(literal -1/2 binary64)) #s(literal 1 binary64))))

Outputs
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))

Calls

3 calls:

2.0ms	x
2.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))
1.0ms	(cos.f64 x)

Results

Accuracy	Segments	Branch
99.8%	1	`(cos.f64 x)`
99.8%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
99.8%	1	`x`

Compiler

Compiled 7 to 7 computations (0% saved)

regimes4.0ms (0.1%)

Memory

11.4MiB live, 11.4MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- 1 (cos x)) (.f64 (.f64 #s(literal 1/2 binary64) x) x))
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))

Outputs
#s(approx (- 1 (cos x)) (.f64 (.f64 #s(literal 1/2 binary64) x) x))

Calls

3 calls:

2.0ms	x
1.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))
1.0ms	(cos.f64 x)

Results

Accuracy	Segments	Branch
99.3%	1	`(cos.f64 x)`
99.3%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
99.3%	1	`x`

Compiler

Compiled 7 to 7 computations (0% saved)

regimes3.0ms (0%)

Memory

7.9MiB live, 7.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))

Outputs
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))

Calls

3 calls:

1.0ms	x
1.0ms	(-.f64 #s(literal 1 binary64) (cos.f64 x))
1.0ms	(cos.f64 x)

Results

Accuracy	Segments	Branch
50.1%	1	`(cos.f64 x)`
50.1%	1	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
50.1%	1	`x`

Compiler

Compiled 7 to 7 computations (0% saved)

simplify14.0ms (0.2%)

Memory

-18.7MiB live, 26.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	51
1	33	51
2	43	51
3	50	51
4	54	51
5	61	51
6	62	51

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
#s(approx (- 1 (cos x)) (.f64 (.f64 #s(literal 1/2 binary64) x) x))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))

Outputs
#s(approx (- 1 (cos x)) (.f64 (fma.f64 (.f64 x x) (fma.f64 (.f64 #s(literal 1/720 binary64) x) x #s(literal -1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
#s(approx (- 1 (cos x)) (.f64 (.f64 #s(literal 1/2 binary64) x) x))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))

derivations453.0ms (7.7%)

Memory

5.7MiB live, 437.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	102
1	119	102
2	317	102
3	1130	102
4	2687	102
5	4996	102
0	8365	90
0	25	148
0	41	148
1	166	148
2	1224	148
0	8367	148

Stop Event

1×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit

Compiler

Compiled 51 to 23 computations (54.9% saved)

preprocess31.0ms (0.5%)

Memory: 16.4MiB live, 61.1MiB allocated
Remove: (abs x)
Compiler: Compiled 170 to 94 computations (44.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze4.0ms (0.1%)

sample3.0s (51%)

explain177.0ms (3%)

preprocess15.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize49.0ms (0.8%)

series1.0ms (0%)

simplify161.0ms (2.7%)

rewrite192.0ms (3.3%)

eval19.0ms (0.3%)

prune23.0ms (0.4%)

simplify297.0ms (5%)

localize232.0ms (3.9%)

series8.0ms (0.1%)

simplify185.0ms (3.1%)

rewrite278.0ms (4.7%)

eval156.0ms (2.6%)

prune21.0ms (0.4%)

simplify31.0ms (0.5%)

localize123.0ms (2.1%)

series4.0ms (0.1%)

simplify157.0ms (2.7%)

rewrite181.0ms (3.1%)

eval38.0ms (0.6%)

prune6.0ms (0.1%)

regimes19.0ms (0.3%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0%)

simplify14.0ms (0.2%)

derivations453.0ms (7.7%)

preprocess31.0ms (0.5%)

end0.0ms (0%)

Profiling